215 research outputs found
On The Dependence Structure of Wavelet Coefficients for Spherical Random Fields
We consider the correlation structure of the random coefficients for a wide
class of wavelet systems on the sphere (Mexican needlets) which were recently
introduced in the literature by Geller and Mayeli (2007). We provide necessary
and sufficient conditions for these coefficients to be asymptotic uncorrelated
in the real and in the frequency domain. Here, the asymptotic theory is
developed in the high resolution sense. Statistical applications are also
discussed, in particular with reference to the analysis of cosmological data.Comment: Revised version for Stochastic Processes and their Application
High-Frequency Tail Index Estimation by Nearly Tight Frames
This work develops the asymptotic properties (weak consistency and
Gaussianity), in the high-frequency limit, of approximate maximum likelihood
estimators for the spectral parameters of Gaussian and isotropic spherical
random fields. The procedure we used exploits the so-called mexican needlet
construction by Geller and Mayeli in [Geller, Mayeli (2009)]. Furthermore, we
propose a plug-in procedure to optimize the precision of the estimators in
terms of asymptotic variance.Comment: 38 page
Gaussian semiparametric estimates on the unit sphere
We study the weak convergence (in the high-frequency limit) of the parameter
estimators of power spectrum coefficients associated with Gaussian, spherical
and isotropic random fields. In particular, we introduce a Whittle-type
approximate maximum likelihood estimator and we investigate its asympotic weak
consistency and Gaussianity, in both parametric and semiparametric cases.Comment: Published in at http://dx.doi.org/10.3150/12-BEJ475 the Bernoulli
(http://isi.cbs.nl/bernoulli/) by the International Statistical
Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm
Needlet-Whittle Estimates on the Unit Sphere
We study the asymptotic behaviour of needlets-based approximate maximum
likelihood estimators for the spectral parameters of Gaussian and isotropic
spherical random fields. We prove consistency and asymptotic Gaussianity, in
the high-frequency limit, thus generalizing earlier results by Durastanti et
al. (2011) based upon standard Fourier analysis on the sphere. The asymptotic
results are then illustrated by an extensive Monte Carlo study.Comment: 48 pages, 2 figure
The needlets bispectrum
The purpose of this paper is to join two different threads of the recent
literature on random fields on the sphere, namely the statistical analysis of
higher order angular power spectra on one hand, and the construction of
second-generation wavelets on the sphere on the other. To this aim, we
introduce the needlets bispectrum and we derive a number of convergence
results. Here, the limit theory is developed in the high resolution sense. The
leading motivation of these results is the need for statistical procedures for
searching non-Gaussianity in Cosmic Microwave Background radiation.Comment: Published in at http://dx.doi.org/10.1214/08-EJS197 the Electronic
Journal of Statistics (http://www.i-journals.org/ejs/) by the Institute of
Mathematical Statistics (http://www.imstat.org
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